Physics – Computational Physics
Scientific paper
2010-05-02
Physics
Computational Physics
36 pages, 5 figures, simplified derivation, a more general mean-force formula, add discussions to the window size, add extensi
Scientific paper
We present an identity that provides an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral. We show that the mean force can be evaluated as a configuration average, and the optimal window size is roughly the inverse of the local mean-force fluctuation. The new identity offers a more robust and precise estimate than a previous work by Adib and Jarzynski [J. Chem. Phys. (122): 14114, 2005]. It also allows a straightforward generalization to an arbitrary ensemble and a joint distribution of multiple variables. Particularly we derive a mean-force enhanced version of the weighted histogram analysis method (WHAM). The method can be used to improve distributions computed from molecular simulations. We illustrate the use in computing a potential energy distribution, a volume distribution in a constant pressure ensemble, a radial distribution function and a joint distribution of amino acid backbone dihedral angles.
Ma Jianpeng
Zhang Cheng
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